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O seguinte trabalho procura estudar problemas de fronteira móvel, conhecidos por problemas de Stefan, bem como aproximar suas soluções. Aplicações de problemas de Stefan encontram-se, por exemplo, na física termal de mudança de estados, presente em diversos fenômenos físicos e químicos naturais e na indústria. Devido a não-linearidade, a maior parte destes problemas não possuem solução analítica conhecida e uma técnica comum para se aproximar soluções é o método de balanceamento integral, inicialmente estudado por Goodman (1958). Este método e suas variações propõem perfis de aproximação no domínio da solução e resolvem uma versão integral da equação diferencial. O problema se resume a resolver uma equação diferencial ordinária no tempo envolvendo a profundidade de penetração do calor e o perfil de aproximação proposto. O trabalho estuda tais métodos para problemas termais clássicos em primeiro lugar, de modo que a extensão para problemas de Stefan seja natural. Refinamentos são apresentados, bem como uma técnica de subdivisão do espaço que resulta num esquema numérico. A técnica de imobilização e fronteira é desenvolvida e aplicada em diversos momentos, a fim de simplificar a utilização dos métodos integrais. / The current work aims to study moving boundary problems, known as Stefan problems, and approximate their solutions. Applications of Stefan problems are found in situations where there is change of physical state, present in several natural and industrial physical and chemical phenomena. Due to their inherent nonlinearity, most of these problems have no known analytic solution and a common technique to approximate solutions is the heat balance integral method, originally studied by Goodman (1958). This method and its variations propose an approximating profile and solve an integral version of the differential equation. The problem is reduced to solving an ordinary differential equation in time involving the depth of heat penetration and the proposed profile. This work studies such classic methods to thermal problems first, in a way that the extension to Stefan problems is natural. Refinements are presented, as well as a technique of subdividing the space domain which results in a numerical scheme. The technique of boundary immobilization is developed and applied at different times in order to simplify the use of these methods.

Zugl.: München, Universiẗat, Diss., 2008.

Thesis (M.F.A.)--Rochester Institute of Technology, 2007. / Typescript. Includes bibliographical references (leaf 40).

O seguinte trabalho procura estudar problemas de fronteira móvel, conhecidos por problemas de Stefan, bem como aproximar suas soluções. Aplicações de problemas de Stefan encontram-se, por exemplo, na física termal de mudança de estados, presente em diversos fenômenos físicos e químicos naturais e na indústria. Devido a não-linearidade, a maior parte destes problemas não possuem solução analítica conhecida e uma técnica comum para se aproximar soluções é o método de balanceamento integral, inicialmente estudado por Goodman (1958). Este método e suas variações propõem perfis de aproximação no domínio da solução e resolvem uma versão integral da equação diferencial. O problema se resume a resolver uma equação diferencial ordinária no tempo envolvendo a profundidade de penetração do calor e o perfil de aproximação proposto. O trabalho estuda tais métodos para problemas termais clássicos em primeiro lugar, de modo que a extensão para problemas de Stefan seja natural. Refinamentos são apresentados, bem como uma técnica de subdivisão do espaço que resulta num esquema numérico. A técnica de imobilização e fronteira é desenvolvida e aplicada em diversos momentos, a fim de simplificar a utilização dos métodos integrais. / The current work aims to study moving boundary problems, known as Stefan problems, and approximate their solutions. Applications of Stefan problems are found in situations where there is change of physical state, present in several natural and industrial physical and chemical phenomena. Due to their inherent nonlinearity, most of these problems have no known analytic solution and a common technique to approximate solutions is the heat balance integral method, originally studied by Goodman (1958). This method and its variations propose an approximating profile and solve an integral version of the differential equation. The problem is reduced to solving an ordinary differential equation in time involving the depth of heat penetration and the proposed profile. This work studies such classic methods to thermal problems first, in a way that the extension to Stefan problems is natural. Refinements are presented, as well as a technique of subdividing the space domain which results in a numerical scheme. The technique of boundary immobilization is developed and applied at different times in order to simplify the use of these methods.

Stefan Zweig et l’Histoire, Stefan Zweig et l’Humain. Le rapport de Zweig à l’Histoire est en corrélation permanente avec l’être humain. Le collectif et l’individuel sont liés dans ses œuvres. Ses récits de vie au tournant des années 1920-1930, ses ouvrages marquant un certain engagement après l’arrivée d’Hitler au pouvoir ou encore le récit de sa propre vie et de son monde, une fois exilé : autant d’œuvres littéraires qui témoignent de l’intérêt de Zweig pour l’Histoire et pour son monde. Zweig s’identifie souvent aux personnages sur lesquels il écrit, retrouvant en eux des similitudes avec sa propre personne, ou bien admirant les qualités de l’un, enviant le courage d’un autre. Les qualités humaines priment à ses yeux, les héros peuvent être de nature différentes ; les héros ne sont pas seulement ceux dont se souviennent les livres d’école. L’intérêt de Zweig pour l’Histoire passée s’explique par son intérêt pour l’époque dans laquelle il vit. Toutefois, Zweig regrette son propre passé et semble également chercher dans les figures de l’Histoire un lien avec le monde perdu, le monde d’hier. Zweig dit avoir eu trois vies. La dernière se termine dans l’exil. Mais comment vivre loin de son monde, de son histoire, de son passé ? / Stefan Zweig and History, Stefan Zweig and Human. The relationship between Zweig and History is in permanent correlation with the human being. The collective and the individual are linked in his works. His stories of life at the turn of the years 1920-1930, his works which mark a certain engagement after the arrival to power of Hitler or the story of his own life and of his world, after his exile: so many literary works that testify of the interest of Zweig for History and for his world. Zweig often identifies himself with the characters about whom he writes, finding in these characters similarities with his own person, or admiring the qualities of some, and envying the courage of others. The human qualities are more important to his eyes, the heroes could be of different nature; heroes aren't only those about whom the school books speak. The interest of Zweig for History is explained by his interest for the time in which he lives. However, Zweig regrets his own past and seems to search, in the characters of History, for a link with his lost world, the world of yesterday. Zweig says that he has had three lives. The last life ends in exile. But how is it possible to live away from our world, from our history, from our past?

Der renommierte Schriftsteller Stefan Heym wäre am 10. April 100 Jahre alt geworden. Um dies zu würdigen, organisiert die Stadt Chemnitz unter Federführung der Internationalen Stefan-Heym-Gesellschaft in seiner Geburtsstadt Chemnitz dieses Jahr eine Reihe von Aktivitäten.

Der renommierte Schriftsteller Stefan Heym wäre am 10. April 100 Jahre alt geworden. Um dies zu würdigen, organisiert die Stadt Chemnitz unter Federführung der Internationalen Stefan-Heym-Gesellschaft in seiner Geburtsstadt Chemnitz dieses Jahr eine Reihe von Aktivitäten.

Some protein gels are products of the dairy industry and some are used as pH-sensitive gels for the controlled delivery of biologically active substances. To understand the dynamics of drug delivery it is very important to establish a mathematical model of protein gel swelling. This required the identification and integration of theory and equations from a wide range of topics. The aim of this research was to develop a mathematical model of transport in polyelectrolyte gels (using the example of β-lactoglobulin protein gels). A complete mathematical model of protein gel swelling was established. The swelling process of protein gels in this thesis involved multicomponent diffusion, chemical ionisation and mechanical deformation. Diffusion of electrolyte solutions through protein gels was modelled using the generalised Maxwell-Stefan (GMS) equation. The swelling pressure as a driving force in the GMS equation was described by rubber elasticity theory. Thermodynamic factors including the charged protein effect were considered in the GMS equation. The model included pH as a variable so it could be applied to both acidic and alkaline cases. The model yielded a set of partial differential equations with algebraic equations for which COMSOL was selected as the simulation software. Although it was found that COMSOL could not always solve the model equations, numerical solutions were obtained for several cases. The model predicted that the equilibrium swelling degree of the gel decreased with high concentration of salts in the bulk solution. The model also predicted that the non-ideal effects were not always small and they depended on the activity coefficients of the species. Satisfactory solutions could not be obtained for all cases using commercial software such as COMSOL Multiphysics. It was shown that COMSOL did not conserve mass but conservativeness was critical in this application because pH and hence the net protein charge is very sensitive to the mass of hydrogen present. In the future, research should be carried out to improve the pressure model in the GMS equation. Theoretical research on Manning condensation theory should be done to modify Manning’s model for more robust prediction of activities of water and ions with protein, and experiments should be done to validate the performance of the modified Manning model. Efforts should be made to write the programming code for a finite volume method to solve the system in three dimensions.